THE TRANSVERSE MERCATOR PROJECTION

Abstract

I. Introduction.—Map projection is a branch of applied mathematics which owes much to J. H. Lambert (v. this Review, i, 2, 91). In his “Beyträge zum Gebrauche der Mathematik und deren Anwendung” (Berlin, 1772) he arrived at a form of projection whereof the Transverse Mercator is a special case, and pointed out that this special case is adapted to a country of great extent in latitude but of small longitudinal width. Germain (“Traité des Projections”, Paris, 1865) described it as the Projection cylindrique orthomorphe de Lambert, but he also introduced the name Projection de Mercator transverse or renversée; he shows that Lambert's treatment of the projection was remarkably simple.     

BOWDITCH TRAVERSE ADJUSTMENT AND A MODIFICATION: NOTES

Abstract

In the second part of the paper on this subject in the last issue (30, 483) the references to the relative angular and linear closures are rather misleading. Mr Clendinning points out that the probable angular error at a station must be considered; the mean error is clearly different.     

SOME PROBLEMS OF RESECTION AND COUNTERSECTION-I

Abstract

“A Well-Defined mountain, though miles inland and never visited by the surveyors, will often prove the very keystone of a chart which cannot be regularly and theoretically triangulated” (“Hydrographic Surveying”, by Rear-Adm. Sir Wm J. L. Wharton, K.C.B., and Rear-Adm. Mostyn Field, F.R.S. 3rd Ed. 1909, p. 128). To many the reasons prohibiting the occupation of inland stations may be unknown; it may suffice to state that, in the past, British hydrographers have mapped many coastal waters where penetration of the land was at least inadvisable. Since the charts so made were in general sold to the world, seamen of all nations have benefited from the surveys.     

Enriching the semantics of the directed polyline–polygon topological relationships: the $$\mathcal {}$$-intersection matrix

In this paper, we define an intersection matrix for enriching the semantics of the topological relationships between a directed polyline and a polygon. In particular, we propose the \(\mathcal {DLP}\)-intersection matrix which enables us to model the origin and destination points, as well as the right- and left-hand sides of the directed polyline. This matrix overcomes the limitation of the well-known DE-9IM, because it allows the representation of the different dimensions of the intersection results at the same time. Accordingly, the geo-operators have been revised and extended in order to address the notions of right- and left-hand sides of a directed polyline, as well as additional notions related to the orientation of the polyline. The \(\mathcal {DLP}\)-intersection matrix has been implemented by extending the Java Topology Suite methods in order to address the new geo-operators based on the notion of orientation.     

A comparative analysis of pansharpening techniques on QuickBird and WorldView-3 images

Nowadays, different image pansharpening methods are available, which combine the strengths of different satellite images that have different spectral and spatial resolutions. These different image fusion methods, however, add spectral and spatial distortions to the resultant images depending on the required context. Therefore, a careful selection of the fusion method is required. Simultaneously, it is also essential that the fusion technique should be efficient to cope with the large data. In this paper, we investigated how different pansharpening algorithms perform, when applied to very high-resolution WorldView-3 and QuickBird satellite images effectively and efficiently. We compared these 27 pansharpening techniques in terms of quantitative analysis, visual inspection and computational complexity, which has not previously been formally tested. In addition, 12 different image quality metrics available in literature are used for quantitative analysis purpose.     

A Novel Approach of Despeckling SAR Images Using Nonlocal Means Filtering

Synthetic aperture radar (SAR) is a day and night, all weather satellite imaging technology. Inherent property of SAR image is speckle noise which produces granular patterns in the image. Speckle noise occurs due to the interference of backscattered echo from earth’s rough surface. There are various speckle reduction techniques in spatial domain and transform domain. Non local means filtering (NLMF) is the technique used for denoising which uses Gaussian weights. In NLMF algorithm, the filtering is performed by taking the weighted mean of all the pixels in a selected search area. The weight given to the pixel is based on the similarity measure calculated as the weighted Euclidean distance over the two windows. Non local means filtering smoothes out homogeneous areas but edges are not preserved. So a discontinuity adaptive weight is used in order to preserve heterogeneous areas like edges. This technique is called as discontinuity adaptive non local means filtering and is well-adapted and robust in the case of Additive White Gaussian Noise (AWGN) model. But speckle is a multiplicative random noise and hence Euclidean distance is not a good choice. This paper presents evaluation results of using different distance measures for improving the accuracy of the Non local means filtering technique. The results are verified using real and synthetic images and from the results it can be concluded that the usage of Manhattan distance improves the accuracy of NLMF technique. Non local approach is used as a preprocessing or post processing technique for many denoising algorithms. So improving NLMF technique would help improving many of the existing denoising techniques.     

Spin rate estimation of sounding rockets using GPS wind-up

Carrier phase wind-up is a well-known effect that arises from the relative rotation between a transmitting and receiving antenna. In GPS measurements at L1 frequency, this effect translates into an error of 19.029 cm per full relative rotation of antennas. Since this effect is independent of the satellite elevation for pure rotation about the antenna boresight axis, it is usually absorbed by the clock estimation in navigation algorithms. Therefore, the impact of wind-up is usually neglected for applications that do not require accuracies to the cm level like RTK. However, in receiving platforms with high rotation rate, the accumulated wind-up value can be important and actually be larger than receiver noise or even ionospheric variations. Therefore, in such scenarios, the wind-up contribution can be isolated and used as a source of information to compute the spin rate of such platforms using an appropriate combination of GPS observables. This work shows some results of a coarse, yet simple, approach to monitor the rotation angle and spin-rate of spin stabilized sounding rockets flown by DLR.     

Population growth and the development of a central place system

This paper describes the spatial and functional evolution of a central place system as market conditions change with population growth. Utilizing a partial equilibrium optimization model, we examine the spatial response of two economic sectors to increases in market populations resulting from natural increase and migration. Response in both sectors is conditioned by threshold demand, with factor prices also affecting one of the sectors. As the central place system evolves it exhibits spatial and functional characteristics that are initially consistent with a Löschian landscape, then a Christallerian landscape at higher populations, while at even larger populations Krugman’s landscape emerges.     

Feature Extraction in Remote Sensing High-Dimensional Image Data

High-dimensional image data open new possibilities in remote sensing digital image classification, particularly when dealing with classes that are spectrally very similar. The main problem refers to the estimation of a large number of classifier's parameters. One possible solution to this problem consists in reducing the dimensionality of the original data without a significant loss of information. In this letter, a new approach to reduce data dimensionality is proposed. In the proposed methodology, each pixel's curve of spectral response is initially segmented, and the digital numbers (DNs) at each segment are replaced by a smaller number of statistics. In this letter, the proposed statistics are the mean and variance of the segment's DNs, which are supposed to carry information about the segment's position and shape, respectively. Tests were performed by using Airborne Visible/Infrared Imaging Spectrometer hyperspectral image data. The experiments have shown that this methodology is capable of providing very acceptable results, in addition of being computationally efficient